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Relaxed hyperelastic curves

Tom 102 / 2011

Annales Polonici Mathematici 102 (2011), 223-230 MSC: 53A04, 53A05, 53C22, 74B20. DOI: 10.4064/ap102-3-3

Streszczenie

We define relaxed hyperelastic curve, which is a generalization of relaxed elastic lines, on an oriented surface in three-dimensional Euclidean space $E^{3}$, and we derive the intrinsic equations for a relaxed hyperelastic curve on a surface. Then, by examining relaxed hyperelastic curves in a plane, on a sphere and on a cylinder, we show that geodesics are relaxed hyperelastic curves in a plane and on a sphere. But on a cylinder, they are relaxed hyperelastic curves only in special cases.

Autorzy

• Ahmet YücesanDepartment of Mathematics
Süleyman Demirel University
32260 Isparta, Turkey
e-mail
• Gözde ÖzkanSüleyman Demirel University
Graduate School of Natural and Sciences
Department of Mathematics
Isparta, Turkey
e-mail
• Yasemín YayDepartment of Mathematics
Giresun University
28100 Giresun, Turkey
e-mail

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